Capacitive position sensing is a common means of detecting displacement in MEMS transducers.
Mechanical parameters of a MEMS device generally determine essential aspects of the transducer design such as sensitivity, noise performance, and MEMS dynamics (resonance frequency, quality factor, settling time etc.). For instance, the mass and the spring of a MEMS device determine the resonance frequency in accordance with the following relationship:
                                          f            res                    =                                                    k                x                            m                                      ,                            Eq        .                                  ⁢                  (          1          )                    Where kx represents the spring, fres represents the resonant frequency and m represents the mass. The damping, b, determines the Brownian noise force as follows:FB=√{square root over (4kBTb)},  Eq. (2)and all three determine the quality factor of the MEMS system, as follows:
                    Q        =                                                                              k                  x                                ⁢                m                                      b                    .                                    Eq        .                                  ⁢                  (          3          )                    
Often, MEMS dynamics are also influenced by factors other than mechanical parameters. For example, a parallel-plate sense capacitor can undesirably introduce electrostatic spring softening. Such a device is often unavoidable especially when MEMS motion is perpendicular to the device layer that the MEMS device is built in. The impact of spring softening can be modeled by an additional spring (kv) acting on the mass. The electrostatic spring constant kv is determined by the second derivative of the sense capacitance with respect to the position and the high-voltage bias (Vb) as follows:
                              k          v                =                              -                          1              2                                ⁢                                                    ⅆ                2                            ⁢                              C                s                                                    ⅆ                              x                2                                              ⁢                                    V              b              2                        .                                              Eq        .                                  ⁢                  (          4          )                    In the presence of spring softening, the resonance frequency of the MEMS system is determined by the sum of all springs acting on the mass, as follows:
                              f          res                =                                                                              k                  x                                +                                  k                  v                                            m                                .                                    Eq        .                                  ⁢                  (          5          )                    
As the bias voltage increases or the parallel-plate gap decreases, spring softening can result in a net negative spring constant causing instability also known as the “pull-in.” At smaller degrees, spring softening can introduce significant variations to resonance frequency and transducer sensitivity. Thus, stability of high-voltage bias and the parallel-plate sense capacitor's gap can become particularly important since they can introduce temperature and package dependence to the transducer via spring softening.
In some prior art techniques, spring softening is avoided in parallel-plate actuators by maintaining a constant charge on the actuator capacitor. In a constant charge actuator, displacement is controlled by the amount of charge stored on the actuator capacitor instead of the voltage difference applied across its terminals. The drive circuit controls the amount of charge flow to the actuator capacitor. Thus, the voltage across the actuator capacitor is free to fluctuate in response to actuator displacements. Such operation, also known as the “charge control”, eliminates position dependence of electrostatic force, and, hence, the spring-softening in parallel-plate actuators.
In contrast to the charge controlled actuator, capacitive sensing often results in charge transfer between the sense capacitor and the capacitance measurement circuit. In a traditional trans-capacitance implementation, the capacitance measurement circuit uses a known capacitance Cfb to convert this charge reading into an output voltage. This scheme however, results in an unwanted position-dependent force and introduces spring softening in the sense capacitor.
There is thus a need for a MEMS capacitive sensing interface with reduced electrostatic spring softening effect.